A279221 Expansion of Product_{k>=1} 1/(1 - x^(k^2*(k+1)/2)).

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 12, 12, 12, 12, 13, 13, 16, 16, 16, 16, 17, 17, 20, 20, 20, 20, 21, 21, 25, 25, 25, 25, 27, 27, 31, 31, 31, 31, 33, 33, 37, 37, 37, 37, 39, 39, 44, 44, 44, 45, 48, 48, 53, 53, 54, 55, 58, 58, 63, 63, 64, 65, 68, 68, 74

Offset

0,7

Comments

Number of partitions of n into nonzero pentagonal pyramidal numbers (A002411).

Links

Table of n, a(n) for n=0..90.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Index to sequences related to pyramidal numbers

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} 1/(1 - x^(k^2*(k+1)/2)).

Example

a(7) = 2 because we have [6, 1] and [1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax=90; CoefficientList[Series[Product[1/(1 - x^(k^2 (k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A002411, A068980, A279220, A279222, A279223, A279224.

Sequence in context: A290792 A279757 A251550 * A357899 A247781 A004052

Adjacent sequences: A279218 A279219 A279220 * A279222 A279223 A279224

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 08 2016

Status

approved